Problem: The sum of two numbers is $42$, and their difference is $10$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 42}$ ${x-y = 10}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 52 $ $ x = \dfrac{52}{2} $ ${x = 26}$ Now that you know ${x = 26}$ , plug it back into $ {x+y = 42}$ to find $y$ ${(26)}{ + y = 42}$ ${y = 16}$ You can also plug ${x = 26}$ into $ {x-y = 10}$ and get the same answer for $y$ ${(26)}{ - y = 10}$ ${y = 16}$ Therefore, the larger number is $26$, and the smaller number is $16$.